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Explore the fascinating world of tensor categories and their role as a new form of "quantum symmetry" in this comprehensive lecture. Delve into how tensor categories generalize classical group symmetry across various fields of mathematics and physics, including quantum groups, quantum topological invariants, quantum information, vertex operator algebras, conformal field theory, and topological order in condensed matter physics. Discover the power of Jones theory of subfactors in operator algebras as a method to study these symmetries. Learn about bi-unitary connections and their application in describing tensor categories using finite dimensional unitary matrices, with a particular focus on their relevance to tensor networks in 2-dimensional topological order. Gain insights into this complex theory without requiring prior knowledge of operator algebras.
